Add Spectra.

thirdparty/include/Spectra/MatOp/SparseGenComplexShiftSolve.h

@@ -0,0 +1,124 @@
+// Copyright (C) 2020-2022 Yixuan Qiu <yixuan.qiu@cos.name>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at https://mozilla.org/MPL/2.0/.
+
+#ifndef SPECTRA_SPARSE_GEN_COMPLEX_SHIFT_SOLVE_H
+#define SPECTRA_SPARSE_GEN_COMPLEX_SHIFT_SOLVE_H
+
+#include <Eigen/Core>
+#include <Eigen/SparseCore>
+#include <Eigen/SparseLU>
+#include <stdexcept>
+
+namespace Spectra {
+
+///
+/// \ingroup MatOp
+///
+/// This class defines the complex shift-solve operation on a sparse real matrix \f$A\f$,
+/// i.e., calculating \f$y=\mathrm{Re}\{(A-\sigma I)^{-1}x\}\f$ for any complex-valued
+/// \f$\sigma\f$ and real-valued vector \f$x\f$. It is mainly used in the
+/// GenEigsComplexShiftSolver eigen solver.
+///
+/// \tparam Scalar_      The element type of the matrix, for example,
+///                      `float`, `double`, and `long double`.
+/// \tparam Flags        Either `Eigen::ColMajor` or `Eigen::RowMajor`, indicating
+///                      the storage format of the input matrix.
+/// \tparam StorageIndex The type of the indices for the sparse matrix.
+///
+template <typename Scalar_, int Flags = Eigen::ColMajor, typename StorageIndex = int>
+class SparseGenComplexShiftSolve
+{
+public:
+    ///
+    /// Element type of the matrix.
+    ///
+    using Scalar = Scalar_;
+
+private:
+    using Index = Eigen::Index;
+    using Vector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
+    using MapConstVec = Eigen::Map<const Vector>;
+    using MapVec = Eigen::Map<Vector>;
+    using SparseMatrix = Eigen::SparseMatrix<Scalar, Flags, StorageIndex>;
+    using ConstGenericSparseMatrix = const Eigen::Ref<const SparseMatrix>;
+
+    using Complex = std::complex<Scalar>;
+    using ComplexVector = Eigen::Matrix<Complex, Eigen::Dynamic, 1>;
+    using SparseComplexMatrix = Eigen::SparseMatrix<Complex, Flags, StorageIndex>;
+
+    using ComplexSolver = Eigen::SparseLU<SparseComplexMatrix>;
+
+    ConstGenericSparseMatrix m_mat;
+    const Index m_n;
+    ComplexSolver m_solver;
+    mutable ComplexVector m_x_cache;
+
+public:
+    ///
+    /// Constructor to create the matrix operation object.
+    ///
+    /// \param mat An **Eigen** sparse matrix object, whose type can be
+    /// `Eigen::SparseMatrix<Scalar, ...>` or its mapped version
+    /// `Eigen::Map<Eigen::SparseMatrix<Scalar, ...> >`.
+    ///
+    template <typename Derived>
+    SparseGenComplexShiftSolve(const Eigen::SparseMatrixBase<Derived>& mat) :
+        m_mat(mat), m_n(mat.rows())
+    {
+        static_assert(
+            static_cast<int>(Derived::PlainObject::IsRowMajor) == static_cast<int>(SparseMatrix::IsRowMajor),
+            "SparseGenComplexShiftSolve: the \"Flags\" template parameter does not match the input matrix (Eigen::ColMajor/Eigen::RowMajor)");
+
+        if (mat.rows() != mat.cols())
+            throw std::invalid_argument("SparseGenComplexShiftSolve: matrix must be square");
+    }
+
+    ///
+    /// Return the number of rows of the underlying matrix.
+    ///
+    Index rows() const { return m_n; }
+    ///
+    /// Return the number of columns of the underlying matrix.
+    ///
+    Index cols() const { return m_n; }
+
+    ///
+    /// Set the complex shift \f$\sigma\f$.
+    ///
+    /// \param sigmar Real part of \f$\sigma\f$.
+    /// \param sigmai Imaginary part of \f$\sigma\f$.
+    ///
+    void set_shift(const Scalar& sigmar, const Scalar& sigmai)
+    {
+        // Create a sparse idendity matrix (1 + 0i on diagonal)
+        SparseComplexMatrix I(m_n, m_n);
+        I.setIdentity();
+        // Sparse LU decomposition
+        m_solver.compute(m_mat.template cast<Complex>() - Complex(sigmar, sigmai) * I);
+        // Set cache to zero
+        m_x_cache.resize(m_n);
+        m_x_cache.setZero();
+    }
+
+    ///
+    /// Perform the complex shift-solve operation
+    /// \f$y=\mathrm{Re}\{(A-\sigma I)^{-1}x\}\f$.
+    ///
+    /// \param x_in  Pointer to the \f$x\f$ vector.
+    /// \param y_out Pointer to the \f$y\f$ vector.
+    ///
+    // y_out = Re( inv(A - sigma * I) * x_in )
+    void perform_op(const Scalar* x_in, Scalar* y_out) const
+    {
+        m_x_cache.real() = MapConstVec(x_in, m_n);
+        MapVec y(y_out, m_n);
+        y.noalias() = m_solver.solve(m_x_cache).real();
+    }
+};
+
+}  // namespace Spectra
+
+#endif  // SPECTRA_SPARSE_GEN_COMPLEX_SHIFT_SOLVE_H